A367171 The sum of divisors of the largest unitary divisor of n that is a term of A138302.

1, 3, 4, 7, 6, 12, 8, 1, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 4, 31, 42, 1, 56, 30, 72, 32, 1, 48, 54, 48, 91, 38, 60, 56, 6, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 3, 72, 8, 80, 90, 60, 168, 62, 96, 104, 1, 84, 144, 68, 126

Offset: 1

Author

Amiram Eldar, Nov 07 2023

Keywords

• nonn
• easy
• mult

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A048298, A138302, A306633, A367168, A367169, A367170.

Similar sequences: A351568, A351569.

Programs

Mathematica

f[p_, e_] := If[e == 2^IntegerExponent[e, 2], (p^(e+1)-1)/(p-1), 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

PARI

a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] == 1 << valuation(f[i, 2], 2), (f[i, 1]^(f[i, 2]+1)-1)/(f[i, 1]-1), 1));}

Formula

Multiplicative with a(p^e) = (p^(A048298(e)+1)-1)/(p-1).

a(n) = A000203(A367168(n)).

a(n) <= A000203(n), with equality if and only if n is in A138302.

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2)/zeta(3) = 1.368432... (A306633).